Polish goalkeeper Boruc failed to deal with Steven Fletcher's tame early deflected strike, which went through his hands on the way into the net.
Strachan refused to criticise the goalkeeper who has got his side out of jail in the past and was left scratching his head about how they managed to leave with no points despite outplaying the capital side for long spells.
"In the number of times we have been to Edinburgh against Hearts and Hibs, that is without doubt the best we have played.
"What I'm seeing at the moment is what I want. I want energy, I want flair and I want variation.
"Am I going away a disappointed man, yes because of the result.
"The performance was fantastic and everyone is scratching their heads.
"We should never have got beaten there."
However, Boruc's afternoon went from bad to worse when Shiels notched the late winner.
Strachan added: "Things like that happen during a game and there is nothing you can do about it as a manager.
"Myself, as a manager, have to deal with a couple of mistakes.
"He does not come in after games for us and say, 'How good am I?', so I would not expect him to get too down on himself."